Optimization of unique batch assembly under parts count uncertainty

In many production environments, batch assembly of unique components is a standard part of the production process. In this analysis, batch assembly of unique components is evaluated under the condition that the quantity of the component parts is a random variable. The purpose of this analysis is to optimize production under the constraint of customer order quantity of final assemblies. Shape and variance of the component part quantity distributions generate variations in optimum order quantity, expected profit and variance of expected profit.;Component part quantity probability distributions analyzed are normal, bimodal, left-truncated normal, right-truncated normal and empirical. To determine optimal input values, computerized numerical optimization methods for statistical analysis and simulation are used. The results provide optimum component part order quantity, expected profit and variance of expected profit for various parameter values. Variables and parameters analyzed include component part order quantity, shape of quantity distribution, standard deviation, customer order quantity range, set-up cost, component part cost, number of components per assembly and selling price of assembly.;Results of the analysis are listed in a set of normalized tables for the distributions and input parameter values examined. Also analyzed is the assumption that as the quantity variance is reduced there will be a corresponding improvement in profit.;The empirical data analyzed show that two of the effects of standard quantity control methods are the creation of the left-truncated normal distribution and the bimodal distribution. The negative effect on profit performance as a result of these distributions is explored. The results suggest methods to reshape distributions, reduce variance and improve profitability.